SOLUTION: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the radius and height are both increasing at the rate of 3 cm/s and 8 cm/s, respectively
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Question 1117082: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the radius and height are both increasing at the rate of 3 cm/s and 8 cm/s, respectively. What is the rate of change of total surface area when its radius and height are 60 cm and 140 cm, respectively? Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! The increase in radius increases the area of the caps and the area of the side wall. The increase in height increases the area of the side wall.
Area of the side wall = 2πrh
Area of the caps = 2πr^2
Now we differentiate to find the rate of change:
dSWA/dt = (2π)(rdh/dt + hdr/dt) + 4πrdr/dt
dSWA/dt = (2π)(60cm * 8 cm/s + 140cm * 3 cm/s) + (4π)(60cm * 3cm/s) = 7916 cm2/s
